Question

If the surface area of a sphere is 2826 cm² then find its volume. (π = 3.14)

Answer 1

Given: Surface area of sphere = 2826 sq.cm. 

To find: Volume of sphere 

Solution:

i. Surface area of sphere = 4πr² 

∴ 2826 = 4 x 3.14 x r² 

2826 = 282600 = 900 

∴  r² = \(\frac{2826}{4\,\times\,3.14}\) = \(\frac{282600}{4\,\times\,314}\)= \(\frac{900}4\)

∴ r² = 225 

∴ r = \(\sqrt{225}\)… [Taking square root on both sides] 

= 15 cm

ii. Volume of sphere = 4/3 πr³ 

= 4/3 x 3.14 x 15 

= 4/3 x 3.14 x 15 x 15 x 15 

= 4 x 3.14 x 5 x 15 x 15 

= 14130 cubic cm. 

∴ The volume of the sphere is 14130 cubic cm.